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Hey there! Let's learn how to compare how different groups of people spend and save their money using random samples.
When we want to know how two large groups spend money, we cannot ask everyone. Instead, we use a random sample. A random sample is a smaller group that fairly represents the whole population.
We can compare two populations by looking at their sample data. For example, we can compare how much money students in Seventh Grade spend on snacks versus students in Eighth Grade.
To compare two groups, we look at their centers, like the median or mean. We also look at how spread out the budgets are. This helps us make a smart guess about the actual populations.
Anish wants to compare how much money seventh-grade and eighth-grade students save each week. He takes a random sample of 10 students from each grade. The 7th-grade sample has a median weekly savings of $5. The 8th-grade sample has a median weekly savings of $8. Compare these two populations based on the samples.
- Identify the two populations being compared: Seventh-grade students and eighth-grade students.
- Find the center (median) of each random sample. The 7th-grade sample median is $5. The 8th-grade sample median is $8.
- Compare the two medians. Subtract the smaller median from the larger median: $8 - $5 = $3.
- Explain the comparison. Based on these samples, we can make an inference that eighth-grade students generally save more money per week than seventh-grade students.
- Note that the typical eighth grader in the sample saves $3 more per week than the typical seventh grader.
